In classical analysis, the Stokes phenomenon refers to the fact that the analytic continuation of asymptotic solutions to certain second-order linear ODEs cannot preserve their asymptotic behaviour. This phenomenon can be interpreted geometrically through meromorphic connections and topologically via Stokes local systems. In this talk, we will first introduce this phenomenon from both geometric and topological perspectives. Then we will explore a wild nonabelian Hodge correspondence, which involves richer geometric structures. A construction of moduli spaces will be presented, and as a result, these spaces are shown hyperkähler. This talk is based on several joint works with Hao Sun.
